I (32f) found out my partner (38m) of 4 years cheated on me a year ago

TW: drugs, alcohol

He’s a musician and plays in a local band, they played out of town this time and at the end of the party they went to sleep in a friend’s house. Few other people came too to continue partying so they were there drinking whisky and also doing coke (I know he does it, never really been an issue since I do it too from time to time).

So fast forward to today, we have been fighting cause he was short on money, I lent him some but found out he lied to me about not doing coke.
I was worried about him and one night he fell asleep before I did so I went through his phone. That’s how I found he cheated on me:
I found this very old chat between him and a girl. Apparently this happened the day after that party.
She sent him her phone number through Instagram asking him to text her. He just answered on Instagram ‘s chat and said “what’s up?”
She asked him if he came inside her and he said “absolutely not 😇”, she seemed worried and asked if she should take precautions and he just said “👍🏻”. Then she said she had a great time and was up to do it again and he sent a random gif of a dog in sunglasses, and that was it.
I mean he’s not a great texter himself so it didnt surprise me.

When I confronted him about it he said he blacked out really bad that night that he didnt even remember doing anything with her and wanted to forget that ever happened saving me the pain since he knows it’s his fault.
He told me he used to see her like 10 years ago and said they never really been friends tho but they did have sex before, he remembers her being at this guy’s house and thinking she became pretty ugly after all those years and that was it. Then he blacked out on alcohol and drugs.

He still claims he doesn’t remember anything about that night but figured something must have happened by her texts. Is it actually possibile to get that fucked up and still have sex?
I mean we had drunk sex and even I had a hard time remembering the act, but I knew I was with a person I wanted to be in the fitst place.
He also said he answered her texts in a cold but “funny” way to get her not to worry or text back ever again, he didn’t even save her number cause he wanted to forget this ever happened.
He has now agreed to get couple therapy.

TLDR: my boyfriend cheated on me while black out drunk and on drugs. This happened once and he has never talked to this person since that night and is now willing to work things out. Is it possible to get fucked up to the point of having sex with someone you don’t like?